Centipawn
The centipawn is the unit of measure used in chess as measure of the advantage. A centipawn is equal to 1/100 of a pawn. Therefore, 100 centipawns = 1 pawn. These values play no formal role in the game but are useful to players, and essentials in computer chess, in order to evaluate positions. The pieces have usually an integer value in pawns, but using the centipawn allows strategic features of the position, worth less than a single pawn, to be evaluated without requiring fractions. Standard Valuation The following is the most common assignment of point values: :The queen is worth 900 :Each rook is worth 500; :Each knight is worth 300; :Each bishop is worth 300; :Each pawn is worth 100 centipawns. The value of the king is undefined as it cannot be captured, let alone traded, during the course of the game. Some early computer chess programs gave the king an arbitrary large value (such as 100,000,000 centipawns) to indicate that the inevitable loss of the king due to checkmate trumps all other considerations. In the endgame, when there is little danger of checkmate, the fighting value of the king is about four pawns. The king is good at attacking and defending nearby pieces and pawns. It is better at defending such pieces than the knight is, and it is better at attacking them than the bishop is. Alternate Valuations Although the 1/3/3/5/9 system of point totals is generally worldwide accepted, many other systems of valuing pieces have been presented. Jacob Sarratt's valuation An 1813 book (source unknown, perhaps by Jacob Sarratt) gives these valuations of the pieces: - Pawn: 2 at the start, 3¾ in the endgame - Knight: 9¼ - Bishop: 9¾ - Rook: 15 - Queen 23¾ - King as attack piece (in the endgame) 6½ which is, converted in centipawns: - Pawn 100 at the start, 187 in the endgame - Knight: 462 - Bishop: 487 - Rook: 750 - Queen: 1,187 This system tends to undervalue the pawns. Howard Staunton's valuation Howard Staunton in The Chess-Player's Handbook notes that piece values are dependent on the position and the phase of the game (the queen typically less valuable toward the endgame), but gives these values, without explaining how they were obtained: - Pawn: 100 - Knight: 305 - Bishop: 350 - Rook: 548 - Queen: 994 Queen and Rook are too much valued here. Paul Rudulf von Biliguer's valuation The 1843 German book Handbuch des Schachspiels by Paul Rudolf von Bilguer gave: - Pawn: 1½ - Knight: 5⅓ - Bishop: 5⅓ - Rook: 8⅔ - Queen: 15½ which converted and normalized are equal to: - Pawn: 100 - Knight: 355 - Bishop: 355 - Rook: 577 - Queen: 1,033 Yevgeny Gik's valuation Yevgeny Gik gave these figures based only on average mobility: - Pawn: 100 - Knight: 240 - Bishop: 400 - Rook: 640 - Queen: 1,040 - King as attacking piece: 300 Emanuel Lasker's valuations World Champion Emanuel Lasker gave the following values here scaled and rounded: - Pawn = 100 (on average) - Knight = 350 - Bishop = 350 (on average) - Rook = 500 (on average) - Queen = 850 However Lasker adjusts some of these depending on the starting positions, with pawns nearer the centre, and bishops/rooks on the kingside, being worth more: - Centre (d/e-file) pawn = 150 points, a/h-file pawn = 50 points - C-file bishop = 350 points, f-file bishop = 375 points - A-file rook = 450 points, h-file rook = 525 points. According to Burgess, Lasker (in his book Lasker's Chess Manual) gave these relative values for the early part of the game: - Rook pawn: 50 - Knight pawn: 125 - Bishop pawn: 150 - Central pawn: 200 - Knight: 450 - Queen bishop: 450 - King bishop: 500 - Queen rook: 600 - King rook: 700 - Queen: 1,100 Larry Evans' valuation Grandmaster Larry Evans gives the values: - Pawn = 100 - Knight = 350 - Bishop = 375 - Rook = 500 - Queen = 1,000 A bishop is usually slightly more powerful than a knight, but not always – it depends on the position. A chess-playing program was given the value of 300 for the knight and 340 for the bishop, but that difference was acknowledged to not be real. Bobby Fisher's Valuation Bobby Fischer gave the values: - Pawn = 100 - Knight = 300 - Bishop = 325 - Rook = 500 - Queen = 900 Larry Kaufman's Research Grandmaster Larry Kaufman performed a computer analysis of thousands of games by masters to determine the average relative value of the pieces. He determined (to the nearest 25 points) the following: - pawn = 100 - knight = 325 - bishop = 325 - rook = 500 - queen = 975 Add an additional 50 point for having both bishops. Kaufman elaborates about how the values of knights and rooks change, depending on the number of pawns on the board: "A further refinement would be to raise the knight's value by 6 and lower the rook's value by 12 for each pawn above five of the side being valued, with the opposite adjustment for each pawn short of five." (Kaufman 1999). Hans Berliner System World Correspondence Chess Champion Hans Berliner gives the following valuations, based on experience and computer experiments: - Pawn = 100 - Knight = 320 - Bishop = 333 - Rook = 510 - Queen = 880 There are adjustments for the rank and file of a pawn and adjustments for the pieces depending on how open or closed the position is. Bishops, rooks, and queens gain up to 10 percent more value in open positions and lose up to 20 percent in closed positions. Knights gain up to 50 percent in closed positions and lose up to 30 percent in the corners and edges of the board. The value of a good bishop may be 10 percent or more than that of a bad bishop. Other Systems Another system is used by Max Euwe and Hans Kramer in Volume 1 of their The Middlegame, with values: - Pawn = 100 - Knight = 350 - Bishop = 350 - Rook = 550 - Queen = 1,000 An early Soviet chess program used: - Pawn = 100 - Knight = 350 - Bishop = 350 - Rook = 500 - Queen = 950 Another popular system is - Pawn = 100 - Knight = 300 - Bishop = 300 - Rook = 450 - Queen = 900 Valuable features Scoring system is essential for chess computers in order to get almost acceptable play. Also humans need to be able to recognize whether the result of many exchanges in a row will be favorable or not, and in order to do that a scoring system is required. Criticism Scoring has mostly been received poorly, although the point system itself falls under similar criticism, as all systems are very rigid and generally fail to take positional factors into account; since the only aim of the game is to checkmate the opponent's king, obviously mere numbers are not enough to describe a particular situation. Also, some openings (called gambits), sacrifice a pawn in order to gain a tempo (e.g. the King's gambit). Category:Scoring Category:Ai